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Mathematical Analysis Lab
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The lab creates new computational algorithms from "solvable" equations such as those describing solitons.
AboutAbout the lab
Applied integrable systems, linking mathematics and computers.
The Mathematical Analysis Lab conducts research ranging from mathematics to computer science, with "applied integrable systems" as its keyword.
An integrable system is a nonlinear dynamical system whose solutions can be written down explicitly; the soliton waves traveling on shallow water are a well-known example.
Because computers can handle only discrete values, putting an integrable system on a computer requires discretizing time and space.
Building on the connection between discretized integrable systems and numerical algorithms, the lab works from mathematical theory through to implementation on computers.
Key terms
- Integrable system
- A nonlinear dynamical system that has as many conserved quantities as degrees of freedom and whose solutions can be written down as formulas.
- Discrete integrable system
- An integrable system in which the structure of the solutions is preserved even when time and space take only discrete values.
- Box-ball system
- A model that moves balls in a row of boxes according to fixed rules and reproduces the behavior of solitons.
ResearchResearch themes
Centered on "applied integrable systems," the lab conducts wide-ranging research from mathematical theory to the implementation of algorithms on computers. It clarifies how discrete integrable systems relate to orthogonal function systems and numerical algorithms, and aims to carry those results into engineering.
*Illustrative imageOrthogonal Polynomials and Integrable Systems
Using the close relationship between discrete integrable systems and orthogonal function systems as a foothold, the lab clarifies the mathematical structures that the two share. It also intends to apply the results to engineering.
*Illustrative imageExploring the Rules of Box-Ball Systems
The box-ball system is a model of solitons that can be rewritten as a finite automaton. The lab studies box-ball systems with newly introduced rules, such as the "box-skipping rule" and the "empty-box rule."
*Illustrative imageFrom Integrable Systems to Computational Algorithms
Developing the theory of the discrete Toda lattice makes it possible to create a new algorithm for generalized eigenvalue problems. The discrete Lotka–Volterra equation has given rise to an algorithm for computing the singular values of matrices.
MembersFaculty
The members of the Mathematical Analysis Lab consist of faculty, researchers, doctoral, master's, and undergraduate students, and administrative assistants.As of 2026
- ProfessorSatoshi Tsujimoto
- Associate ProfessorTakafumi Mase
- Assistant ProfessorKatsuki Kobayashi
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “The board” Yulia Meshkova / CC BY 4.0 (cropped)
- Orthogonal Polynomials and Integrable Systems: “Legendre Polynomials” Alan Mak / CC BY-SA 3.0 (cropped)
- Exploring the Rules of Box-Ball Systems: “Soliton hydro” Christophe.Finot et Kamal HAMMANI / CC BY-SA 2.5 (cropped)
- From Integrable Systems to Computational Algorithms: “Jacobi iteration” GlennHK / Public domain (cropped)
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